Handshake Lemma/Examples/No Graph with One Odd Vertex

Examples of Use of Handshake Lemma

There exists no undirected graph with exactly one odd vertex.

Proof

The Handshake Lemma which states that the number of odd vertices in any undirected graph is even.

$\blacksquare$

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $2$: Elementary Concepts of Graph Theory: $\S 2.1$: The Degree of a Vertex: Problem $7 \ \text{(c)}$